This problem presented here is similar to a standard VRP, except that each delivery to a customer is represented by two visits, only one of which can be performed. Each of these visits has a penalty cost for not being performed, and the total cost of the solution includes the penalty cost of the unperformed visits.

The first step is to write a natural language description of the problem.

The components of the routing model for this problem are the same as for a standard VRP: vehicles, customers, and a depot. However, each delivery to a customer is represented by two alternative visits.

The constraints in this problem are the same as those in a standard VRP: time windows, vehicle capacity, and visit quantities.

The objective is to minimize the total cost of the solution. This cost includes the penalty costs for not performing the visit in each pair that is unperformed.